diff --git a/crates/fj-kernel/src/algorithms/sweep/edge.rs b/crates/fj-kernel/src/algorithms/sweep/edge.rs
index f774d1add..29b657983 100644
--- a/crates/fj-kernel/src/algorithms/sweep/edge.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/edge.rs
@@ -95,7 +95,7 @@ impl Sweep for (HalfEdge, Color) {
                 let global = bottom_edge
                     .curve()
                     .global_form()
-                    .clone_object()
+                    .clone()
                     .translate(path, stores);
 
                 // Please note that creating a line here is correct, even if the
diff --git a/crates/fj-kernel/src/algorithms/transform.rs b/crates/fj-kernel/src/algorithms/transform.rs
deleted file mode 100644
index 8166f8ea7..000000000
--- a/crates/fj-kernel/src/algorithms/transform.rs
+++ /dev/null
@@ -1,249 +0,0 @@
-//! Transforming objects
-
-use fj_math::{Transform, Vector};
-
-use crate::{
-    objects::{
-        Curve, Cycle, Face, Faces, GlobalCurve, GlobalEdge, GlobalVertex,
-        HalfEdge, Shell, Sketch, Solid, Surface, SurfaceVertex, Vertex,
-    },
-    path::GlobalPath,
-    stores::{Handle, Stores},
-};
-
-/// Transform an object
-///
-/// # Implementation Note
-///
-/// So far, a general `transform` method is available, along some convenience
-/// methods for more specific transformations.
-///
-/// More convenience methods can be added as required. The only reason this
-/// hasn't been done so far, is that no one has put in the work yet.
-pub trait TransformObject: Sized {
-    /// The type of the transformed object
-    ///
-    /// # Implementation Note
-    ///
-    /// This type is temporary, while we transition to a global object store. It
-    /// should be removed, once that transition is complete.
-    type Transformed;
-
-    /// Transform the object
-    #[must_use]
-    fn transform(
-        self,
-        transform: &Transform,
-        stores: &Stores,
-    ) -> Self::Transformed;
-
-    /// Translate the object
-    #[must_use]
-    fn translate(
-        self,
-        offset: impl Into<Vector<3>>,
-        stores: &Stores,
-    ) -> Self::Transformed {
-        self.transform(&Transform::translation(offset), stores)
-    }
-
-    /// Rotate the object
-    #[must_use]
-    fn rotate(
-        self,
-        axis_angle: impl Into<Vector<3>>,
-        stores: &Stores,
-    ) -> Self::Transformed {
-        self.transform(&Transform::rotation(axis_angle), stores)
-    }
-}
-
-impl TransformObject for Curve {
-    type Transformed = Self;
-
-    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
-        let surface = self.surface().transform(transform, stores);
-        let global = self.global_form().transform(transform, stores);
-
-        // Don't need to transform `self.kind`, as that's in local form.
-        Curve::new(surface, self.path(), global)
-    }
-}
-
-impl TransformObject for Cycle {
-    type Transformed = Self;
-
-    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
-        Self::new(
-            self.surface().transform(transform, stores),
-            self.into_half_edges()
-                .map(|edge| edge.transform(transform, stores)),
-        )
-    }
-}
-
-impl TransformObject for Face {
-    type Transformed = Self;
-
-    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
-        let exterior = self.exterior().clone().transform(transform, stores);
-        let interiors = self
-            .interiors()
-            .map(|cycle| cycle.clone().transform(transform, stores));
-
-        let color = self.color();
-
-        Face::from_exterior(exterior)
-            .with_interiors(interiors)
-            .with_color(color)
-    }
-}
-
-impl TransformObject for Faces {
-    type Transformed = Self;
-
-    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
-        let mut faces = Faces::new();
-        faces.extend(
-            self.into_iter()
-                .map(|face| face.transform(transform, stores)),
-        );
-        faces
-    }
-}
-
-impl TransformObject for GlobalCurve {
-    type Transformed = Handle<Self>;
-
-    fn transform(self, transform: &Transform, stores: &Stores) -> Handle<Self> {
-        stores.global_curves.insert(GlobalCurve::from_path(
-            self.path().transform(transform, stores),
-        ))
-    }
-}
-
-impl TransformObject for GlobalEdge {
-    type Transformed = Self;
-
-    fn transform(
-        self,
-        transform: &Transform,
-        stores: &Stores,
-    ) -> Self::Transformed {
-        let curve = self.curve().clone().transform(transform, stores);
-        let vertices = self
-            .vertices()
-            .map(|vertex| vertex.transform(transform, stores));
-
-        Self::new(curve, vertices)
-    }
-}
-
-impl TransformObject for GlobalPath {
-    type Transformed = Self;
-
-    fn transform(self, transform: &Transform, _: &Stores) -> Self {
-        match self {
-            Self::Circle(curve) => {
-                Self::Circle(transform.transform_circle(&curve))
-            }
-            Self::Line(curve) => Self::Line(transform.transform_line(&curve)),
-        }
-    }
-}
-
-impl TransformObject for GlobalVertex {
-    type Transformed = Self;
-
-    fn transform(self, transform: &Transform, _: &Stores) -> Self {
-        let position = transform.transform_point(&self.position());
-        Self::from_position(position)
-    }
-}
-
-impl TransformObject for HalfEdge {
-    type Transformed = Self;
-
-    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
-        let curve = self.curve().clone().transform(transform, stores);
-        let vertices = self
-            .vertices()
-            .clone()
-            .map(|vertex| vertex.transform(transform, stores));
-        let global_form =
-            self.global_form().clone().transform(transform, stores);
-
-        Self::new(curve, vertices, global_form)
-    }
-}
-
-impl TransformObject for Shell {
-    type Transformed = Self;
-
-    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
-        let faces = self
-            .into_faces()
-            .into_iter()
-            .map(|face| face.transform(transform, stores));
-        Self::new().with_faces(faces)
-    }
-}
-
-impl TransformObject for Sketch {
-    type Transformed = Self;
-
-    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
-        let faces = self
-            .into_faces()
-            .into_iter()
-            .map(|face| face.transform(transform, stores));
-        Self::new().with_faces(faces)
-    }
-}
-
-impl TransformObject for Solid {
-    type Transformed = Self;
-
-    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
-        let faces = self
-            .into_shells()
-            .map(|shell| shell.transform(transform, stores));
-        Self::new().with_shells(faces)
-    }
-}
-
-impl TransformObject for Surface {
-    type Transformed = Self;
-
-    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
-        Self::new(
-            self.u().transform(transform, stores),
-            transform.transform_vector(&self.v()),
-        )
-    }
-}
-
-impl TransformObject for SurfaceVertex {
-    type Transformed = Self;
-
-    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
-        Self::new(
-            self.position(),
-            self.surface().transform(transform, stores),
-            self.global_form().transform(transform, stores),
-        )
-    }
-}
-
-impl TransformObject for Vertex {
-    type Transformed = Self;
-
-    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
-        Self::new(
-            self.position(),
-            self.curve().clone().transform(transform, stores),
-            self.surface_form().transform(transform, stores),
-            self.global_form().transform(transform, stores),
-        )
-    }
-}
diff --git a/crates/fj-kernel/src/algorithms/transform/curve.rs b/crates/fj-kernel/src/algorithms/transform/curve.rs
new file mode 100644
index 000000000..dcba67312
--- /dev/null
+++ b/crates/fj-kernel/src/algorithms/transform/curve.rs
@@ -0,0 +1,28 @@
+use fj_math::Transform;
+
+use crate::{
+    objects::{Curve, GlobalCurve},
+    stores::{Handle, Stores},
+};
+
+use super::TransformObject;
+
+impl TransformObject for Curve {
+    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
+        let surface = self.surface().transform(transform, stores);
+        let global_form =
+            self.global_form().clone().transform(transform, stores);
+
+        // Don't need to transform `self.path`, as that's defined in surface
+        // coordinates, and thus transforming `surface` takes care of it.
+        Self::new(surface, self.path(), global_form)
+    }
+}
+
+impl TransformObject for Handle<GlobalCurve> {
+    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
+        stores.global_curves.insert(GlobalCurve::from_path(
+            self.path().transform(transform, stores),
+        ))
+    }
+}
diff --git a/crates/fj-kernel/src/algorithms/transform/cycle.rs b/crates/fj-kernel/src/algorithms/transform/cycle.rs
new file mode 100644
index 000000000..cfcd0975b
--- /dev/null
+++ b/crates/fj-kernel/src/algorithms/transform/cycle.rs
@@ -0,0 +1,15 @@
+use fj_math::Transform;
+
+use crate::{objects::Cycle, stores::Stores};
+
+use super::TransformObject;
+
+impl TransformObject for Cycle {
+    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
+        Self::new(
+            self.surface().transform(transform, stores),
+            self.into_half_edges()
+                .map(|edge| edge.transform(transform, stores)),
+        )
+    }
+}
diff --git a/crates/fj-kernel/src/algorithms/transform/edge.rs b/crates/fj-kernel/src/algorithms/transform/edge.rs
new file mode 100644
index 000000000..a900f0791
--- /dev/null
+++ b/crates/fj-kernel/src/algorithms/transform/edge.rs
@@ -0,0 +1,33 @@
+use fj_math::Transform;
+
+use crate::{
+    objects::{GlobalEdge, HalfEdge},
+    stores::Stores,
+};
+
+use super::TransformObject;
+
+impl TransformObject for HalfEdge {
+    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
+        let curve = self.curve().clone().transform(transform, stores);
+        let vertices = self
+            .vertices()
+            .clone()
+            .map(|vertex| vertex.transform(transform, stores));
+        let global_form =
+            self.global_form().clone().transform(transform, stores);
+
+        Self::new(curve, vertices, global_form)
+    }
+}
+
+impl TransformObject for GlobalEdge {
+    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
+        let curve = self.curve().clone().transform(transform, stores);
+        let vertices = self
+            .vertices()
+            .map(|vertex| vertex.transform(transform, stores));
+
+        Self::new(curve, vertices)
+    }
+}
diff --git a/crates/fj-kernel/src/algorithms/transform/face.rs b/crates/fj-kernel/src/algorithms/transform/face.rs
new file mode 100644
index 000000000..608dbd9b9
--- /dev/null
+++ b/crates/fj-kernel/src/algorithms/transform/face.rs
@@ -0,0 +1,34 @@
+use fj_math::Transform;
+
+use crate::{
+    objects::{Face, Faces},
+    stores::Stores,
+};
+
+use super::TransformObject;
+
+impl TransformObject for Face {
+    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
+        let exterior = self.exterior().clone().transform(transform, stores);
+        let interiors = self
+            .interiors()
+            .map(|cycle| cycle.clone().transform(transform, stores));
+
+        let color = self.color();
+
+        Face::from_exterior(exterior)
+            .with_interiors(interiors)
+            .with_color(color)
+    }
+}
+
+impl TransformObject for Faces {
+    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
+        let mut faces = Faces::new();
+        faces.extend(
+            self.into_iter()
+                .map(|face| face.transform(transform, stores)),
+        );
+        faces
+    }
+}
diff --git a/crates/fj-kernel/src/algorithms/transform/mod.rs b/crates/fj-kernel/src/algorithms/transform/mod.rs
new file mode 100644
index 000000000..c8ce24269
--- /dev/null
+++ b/crates/fj-kernel/src/algorithms/transform/mod.rs
@@ -0,0 +1,47 @@
+//! API for transforming objects
+
+mod curve;
+mod cycle;
+mod edge;
+mod face;
+mod path;
+mod shell;
+mod sketch;
+mod solid;
+mod surface;
+mod vertex;
+
+use fj_math::{Transform, Vector};
+
+use crate::stores::Stores;
+
+/// Transform an object
+///
+/// # Implementation Note
+///
+/// So far, a general `transform` method is available, along some convenience
+/// methods for more specific transformations.
+///
+/// More convenience methods can be added as required. The only reason this
+/// hasn't been done so far, is that no one has put in the work yet.
+pub trait TransformObject: Sized {
+    /// Transform the object
+    #[must_use]
+    fn transform(self, transform: &Transform, stores: &Stores) -> Self;
+
+    /// Translate the object
+    ///
+    /// Convenience wrapper around [`TransformObject::transform`].
+    #[must_use]
+    fn translate(self, offset: impl Into<Vector<3>>, stores: &Stores) -> Self {
+        self.transform(&Transform::translation(offset), stores)
+    }
+
+    /// Rotate the object
+    ///
+    /// Convenience wrapper around [`TransformObject::transform`].
+    #[must_use]
+    fn rotate(self, axis_angle: impl Into<Vector<3>>, stores: &Stores) -> Self {
+        self.transform(&Transform::rotation(axis_angle), stores)
+    }
+}
diff --git a/crates/fj-kernel/src/algorithms/transform/path.rs b/crates/fj-kernel/src/algorithms/transform/path.rs
new file mode 100644
index 000000000..b4c998654
--- /dev/null
+++ b/crates/fj-kernel/src/algorithms/transform/path.rs
@@ -0,0 +1,16 @@
+use fj_math::Transform;
+
+use crate::{path::GlobalPath, stores::Stores};
+
+use super::TransformObject;
+
+impl TransformObject for GlobalPath {
+    fn transform(self, transform: &Transform, _: &Stores) -> Self {
+        match self {
+            Self::Circle(curve) => {
+                Self::Circle(transform.transform_circle(&curve))
+            }
+            Self::Line(curve) => Self::Line(transform.transform_line(&curve)),
+        }
+    }
+}
diff --git a/crates/fj-kernel/src/algorithms/transform/shell.rs b/crates/fj-kernel/src/algorithms/transform/shell.rs
new file mode 100644
index 000000000..d2ebadad9
--- /dev/null
+++ b/crates/fj-kernel/src/algorithms/transform/shell.rs
@@ -0,0 +1,15 @@
+use fj_math::Transform;
+
+use crate::{objects::Shell, stores::Stores};
+
+use super::TransformObject;
+
+impl TransformObject for Shell {
+    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
+        let faces = self
+            .into_faces()
+            .into_iter()
+            .map(|face| face.transform(transform, stores));
+        Self::new().with_faces(faces)
+    }
+}
diff --git a/crates/fj-kernel/src/algorithms/transform/sketch.rs b/crates/fj-kernel/src/algorithms/transform/sketch.rs
new file mode 100644
index 000000000..4a48bb23d
--- /dev/null
+++ b/crates/fj-kernel/src/algorithms/transform/sketch.rs
@@ -0,0 +1,15 @@
+use fj_math::Transform;
+
+use crate::{objects::Sketch, stores::Stores};
+
+use super::TransformObject;
+
+impl TransformObject for Sketch {
+    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
+        let faces = self
+            .into_faces()
+            .into_iter()
+            .map(|face| face.transform(transform, stores));
+        Self::new().with_faces(faces)
+    }
+}
diff --git a/crates/fj-kernel/src/algorithms/transform/solid.rs b/crates/fj-kernel/src/algorithms/transform/solid.rs
new file mode 100644
index 000000000..558e3a1e0
--- /dev/null
+++ b/crates/fj-kernel/src/algorithms/transform/solid.rs
@@ -0,0 +1,14 @@
+use fj_math::Transform;
+
+use crate::{objects::Solid, stores::Stores};
+
+use super::TransformObject;
+
+impl TransformObject for Solid {
+    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
+        let faces = self
+            .into_shells()
+            .map(|shell| shell.transform(transform, stores));
+        Self::new().with_shells(faces)
+    }
+}
diff --git a/crates/fj-kernel/src/algorithms/transform/surface.rs b/crates/fj-kernel/src/algorithms/transform/surface.rs
new file mode 100644
index 000000000..823431256
--- /dev/null
+++ b/crates/fj-kernel/src/algorithms/transform/surface.rs
@@ -0,0 +1,14 @@
+use fj_math::Transform;
+
+use crate::{objects::Surface, stores::Stores};
+
+use super::TransformObject;
+
+impl TransformObject for Surface {
+    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
+        Self::new(
+            self.u().transform(transform, stores),
+            transform.transform_vector(&self.v()),
+        )
+    }
+}
diff --git a/crates/fj-kernel/src/algorithms/transform/vertex.rs b/crates/fj-kernel/src/algorithms/transform/vertex.rs
new file mode 100644
index 000000000..89d2507b6
--- /dev/null
+++ b/crates/fj-kernel/src/algorithms/transform/vertex.rs
@@ -0,0 +1,38 @@
+use fj_math::Transform;
+
+use crate::{
+    objects::{GlobalVertex, SurfaceVertex, Vertex},
+    stores::Stores,
+};
+
+use super::TransformObject;
+
+impl TransformObject for Vertex {
+    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
+        let curve = self.curve().clone().transform(transform, stores);
+        let surface_form = self.surface_form().transform(transform, stores);
+        let global_form = self.global_form().transform(transform, stores);
+
+        // Don't need to transform `self.position`, as that is in curve
+        // coordinates and thus transforming the curve takes care of it.
+        Self::new(self.position(), curve, surface_form, global_form)
+    }
+}
+
+impl TransformObject for SurfaceVertex {
+    fn transform(self, transform: &Transform, stores: &Stores) -> Self {
+        let surface = self.surface().transform(transform, stores);
+        let global_form = self.global_form().transform(transform, stores);
+
+        // Don't need to transform `self.position`, as that is in surface
+        // coordinates and thus transforming the surface takes care of it.
+        Self::new(self.position(), surface, global_form)
+    }
+}
+
+impl TransformObject for GlobalVertex {
+    fn transform(self, transform: &Transform, _: &Stores) -> Self {
+        let position = transform.transform_point(&self.position());
+        Self::from_position(position)
+    }
+}